High-order difference methods for waves in discontinuous media

Second-, fourth- and sixth-order one-step methods have been constructed for the solution of wave propagation problems. The method is based on the first-order system formulation of the wave equation, and uses a staggered grid both in space and time. The method is applied with good results to a problem with discontinuous coefficients without using any special procedure across the discontinuity. The behavior of the truncation error has been investigated for one-dimensional problems and stability criteria have been derived for one- and two-dimensional cases.